We will be using some JAVA applets to demonstrate the construction of position-time and position velocity diagrams.
The only quantities that you will be able to measure are:
In all cases the motion will be that of Motion Under Constant Acceleration
Some questions to think about are the following:
Let's being by considering the following diagram, which is a position vs time diagram describing the motion of some object under constant acceleration.
This diagram was made by using an appartus known as a fan-cart schematially shown below.
We can define the average velocity as the change in position divided by the change in time or:
which is the slope of the line in the position vs time graph. By graphical means we then determine the velocity at any time by determining the slope on the graph at that time. This is what calculus is about but we aren't doing that here.
So, for instance, the average velocity of the cart over the time interval of 6 to 14 seconds would be equal to 1/4 meter per second (the cart moved 2 meters in 8 seconds).
Where we see that there are obvious changes in the velocity at various times. We are interested in understand what causes these changes in velocity.
In general an acceleration causes a change in velocity and thus we can define an average acceleartion in a manner that is similar to the definition of average velocity. In this case an average acceleration would be the change in velocity over some time interval or
So, for example, over the period 6-8 seconds there was a change in velocity of 1.5 meters per second or an acceleration of:
1.5/2 = 0.75 meters per second2
The fan attachment exerts an almost constant force on the cart. What is the relationship between that strength of that force and the cart's acceleration?
We can qualitatively test this set of conjectures by considering the applet below. First set the friction slider to 0.
Then select a Force and Select a mass. Try to use different forces with the same mass or different masses with the same force. Observe the behavior of the position vs time and velocity vs time diagrams for different combinations of forces and masses. This should help you understand the relations between force, mass and acceleration.
Finally, turn friction to 0.1 and repeat the measurements. How does the velocity vs time diagram with friction = 0.1 compare to friction = 0.0. Is it linear or is it curved? If its curved, what do you think that means?
Definitions for speed, velocity, acceleration, force and mass in words.